A GUIDE FOR TEACHING MATHEMATICS AT GEORGIA
It is the responsibility of the teacher to actively involve his or her
students in the learning process. The most important thing he or she should
do is to avoid giving clear, concise, organized lectures. If the presentation
of a lesson is too easy to follow, most of the class will not need to learn
the new material on their own. They will have a certain degree of confidence
in their new knowledge, and this will tend to stifle their intellectual
pursuits. If, on the other hand, the lecture is vague, rambling and disorganized,
the students will leave with their heads full of questions. In fact, they
will be so filled with curiosity that they will try to expand their knowledge
on their own.
There are many ways to present a thought provoking lecture. One of
the easiest techniques to use is a foreign accent. If the accent is thick
enough, even a well organized lecture will produce expressions of intellectual
wonder among the students. Effective accents can be acquired in Alabama,
China, India, Latin America, New York City, Germany, or any foreign country.
For natives of Kansas, that is, for individuals who cannot speak anything
but perfect Midwestern English, this technique may offer difficulties.
There are two possible solutions:
After a couple of sentences, most of the class will be staring at their
watches or out the windows. Very quickly, they will become very anxious
to go out and learn the material on their own.
1. One can teach in a foreign country, or at least in New York or
2. One can incorporate a new syllable into one's language. Two very
effective syllables to use are "um" and "uh". The chosen syllable should
be uttered every second or third word. This reduces the possibility that
any coherent concept will be given to the class. For example, on can say,
"Um, today, u..m, we will be, um, discussing, um....um, determinants."
In addition, to being aware of one's own speech patterns, the teacher
should also pay close attention to the written word. Effective use of the
black board should be considered almost a necessity. Illegible handwriting
can stimulate a student's interest in new material almost as effectively
as incoherent lectures. Often students will meet outside of class to exchange
interpretations of lecture notes. Thus illegible handwriting encourages
students to work together and share ideas.
Writing illegibly requires a great deal of practice to be effective.
If one does not have satisfactory handwriting (that is to say, if one's
handwriting is suitable only for formal invitations and eye charts), certain
"tricks" can be learned:
There is one last point on teaching technique. It is important that one
does not overprepare for lectures. Generally, one should arrive at class
a few minutes early, open the book, and glance at the topic for that particular
day. Lectures prepared in this manner have a certain freshness and spontaneity
that is often mission from those which are more carefully organized. In
addition, students will gain a greater appreciation for a correct proof
is they see how much time can be spent on a wrong approach.
1. Write small. For students in the back rows, this is almost as
effective as writing illegibly. The disadvantage is that students in the
front rows will probably be able to read the board and may possibly learn
something without having to spend hours interpreting their notes. Also,
the professor who writes small may find that most of his or her class will
try to sit near the front of the room, which may be too close for comfort,
especially on hot days during summer sessions.
2. Write fast. The faster the teacher writes, the faster the students
will have to take notes. Often the teacher can move on the a new subject
while his or her students are still trying to copy what is on the board.
Students will be so busy during class that they will wait until after class
to try to understand the lesson. In addition to spurring students to learn
on their own, writing fast allows the professor to cover more material
in a given class period.
3. Write something while saying something different. For example,
after working out a lengthy problem the instructor tells the class the
answer is x^2 + y while writing on the board y^2 + x. This forces students
to rethink the problem in order to d ecide which alternative is correct.
Students are thus actively involved in problem solving even after the problem
4. Erase quickly. This technique practically forces those members
of the class who take notes to pay constant attention to the lectures.
Those who doze off for a few moments will awaken to find nothing to record
in their notes on the topics they missed. This technique is especially
effective if one uses both hands to write and erase simultaneously.
5. If all else fails, stand in front of what has just been written.
By blocking any clear view of the blackboard, the teacher will help improve
students' speculative and psychic abilities. Those instructors who are
short or underweight may find this procedure extremely difficult.
6. The above "tricks" may be used separately or combined. It is a
good idea to change them occasionally in order to add some variety to the
7. It is very important that the professor lecture to the blackboard
when using it. This helps demonstrate to students how involved the teacher
is with the subject. This enthusiasm will most assuredly rub off on the
class. Also, by facing the blackboard, one cannot face the class. It is
therefore easier to ignore students' questions which tend to interrupt
the presentation of topics and make the class period seem to last forever.
The first section of this guide has dealt with actual teaching, concentrating
on lecturing "tricks", techniques, and preparation. The subject of the
last part will be general appearances.
Students tend to have more confidence in an instructor if they believe
he or she has a thorough understanding of his or her field. To show a class
that one has a thorough understanding of mathematics, it is necessary to
appear "spaced-out." Being "spaced-out" implies one is so involved with
abstract mathematics that one has lost touch with the real world. There
are several ways to project such an image.
By being properly "spaced-out", one will gain the confidence and respect
of one's students. This will make it easier to help inspire them in their
study of mathematics. Being properly "spaced-out" will also help one to
acquire tenure at this or any other reputable college or university.
1. Dress funny. Old suits, baggy pants, narrow ties, and hairy sweaters
are all effective and even more so, when worn together.
2. Don't wash your sweatshirts. Albert Einstein is best remembered
for two things -- being a genius and wearing dirty sweatshirts. Even if
you are not a genius, you can still wear the sweatshirts. In a matter of
weeks, you will gain such a reputation that no one will come near enough
to challenge it.
3. Don't comb your hair with anything finer than your left hand.
4. Walk into the wrong room and begin to lecture to whatever class
is in it. (This will help spread your reputation beyond your own students).
5. Walk into the correct classroom and begin lecturing on whatever
happens to be left on the black board from the previous class.
6. Acquire a facial twitch.
7. Pretend you are deaf if someone asks a question or the bell rings
while you are lecturing. Try to keep talking after everyone has left the
8. Follow all the guidelines for teaching given above.